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21
Multidimensional Access Methods
, 1998
"... Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that ..."
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Cited by 561 (3 self)
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Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 421 (11 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
Querying multidimensional data indexed using the hilbert spacefilling curve
 SIGMOD Record
, 2001
"... Mapping to onedimensional values and then using a onedimensional indexing method has been proposed as a way of indexing multidimensional data. Most previous related work uses the ZOrder Curve but more recently the Hilbert Curve has been considered since it has superior clustering properties. Any ..."
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Cited by 25 (0 self)
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Mapping to onedimensional values and then using a onedimensional indexing method has been proposed as a way of indexing multidimensional data. Most previous related work uses the ZOrder Curve but more recently the Hilbert Curve has been considered since it has superior clustering properties. Any approach, however, can only be of practical value if there are e ective methods for executing range and partial match queries. This paper describes such amethod for the Hilbert Curve. 1
A Fast Similarity Join Algorithm Using Graphics Processing Units
"... Abstract — A similarity join operation A ⋊⋉ɛ B takes two sets of points A, B and a value ɛ ∈ R, and outputs pairs of points p ∈ A, q ∈ B, such that the distance D(p, q) ≤ ɛ. Similarity joins find use in a variety of fields, such as clustering, text mining, and multimedia databases. A novel similari ..."
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Cited by 22 (0 self)
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Abstract — A similarity join operation A ⋊⋉ɛ B takes two sets of points A, B and a value ɛ ∈ R, and outputs pairs of points p ∈ A, q ∈ B, such that the distance D(p, q) ≤ ɛ. Similarity joins find use in a variety of fields, such as clustering, text mining, and multimedia databases. A novel similarity join algorithm called LSS is presented that executes on a Graphics Processing Unit (GPU), exploiting its parallelism and high data throughput. As GPUs only allow simple data operations such as the sorting and searching of arrays, LSS uses these two operations to cast a similarity join operation as a GPU sortandsearch problem. It first creates, on the fly, a set of spacefilling curves on one of its input datasets, using a parallel GPU sort routine. Next, LSS processes each point p of the other dataset in parallel. For each p, it searches an interval of one of the spacefilling curves guaranteed to contain all the pairs in which p participates. Using extensive theoretical and experimental analysis, LSS is shown to offer a good balance between time and work efficiency. Experimental results demonstrate that LSS is suitable for similarity joins in large highdimensional datasets, and that it performs well when compared against two existing prominent similarity join methods. I.
Space Filling Curves and Their Use in the Design of Geometric Data Structures
"... . We are given a twodimensional square grid of size N \Theta N , where N := 2 n and n 0. A space filling curve (SFC) is a numbering of the cells of this grid with numbers from c + 1 to c +N 2 , for some c 0. We call a SFC recursive (RSFC) if it can be recursively divided into four square RSFC ..."
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Cited by 17 (1 self)
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. We are given a twodimensional square grid of size N \Theta N , where N := 2 n and n 0. A space filling curve (SFC) is a numbering of the cells of this grid with numbers from c + 1 to c +N 2 , for some c 0. We call a SFC recursive (RSFC) if it can be recursively divided into four square RSFCs of equal size. Examples of wellknown RSFCs include the Hilbert curve, the zcurve, and the Gray code. We prove several useful and interesting combinatorial properties of recursive and general SFCs. In addition, we describe grammars for generating RSFCs. For certain optimality criteria, we propose optimal RSFCs. In addition, for an optimality criterion that is important in the design of geometric data structures, we propose a RSFC that outperforms the previously known RSFCs in the worstcase. 1 Introduction Data structures for maintaining sets of multidimensional points on external storage play an important role in many nonstandard database systems, where query performance is still a maj...
The Application of Spacefilling Curves to the Storage and Retrieval of Multidimensional Data
, 2000
"... Indexing of multidimensional data has been the focus of a considerable amount of research effort over many years but no generally agreed paradigm has emerged to compare with the impact of the BTree, for example, on the indexing of onedimensional data. At the same time, the need for efficient meth ..."
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Cited by 16 (3 self)
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Indexing of multidimensional data has been the focus of a considerable amount of research effort over many years but no generally agreed paradigm has emerged to compare with the impact of the BTree, for example, on the indexing of onedimensional data. At the same time, the need for efficient methods is ever more important in an environment where databases become larger and more complex in their structures. Mapping multidimensional data to one dimension, thus enabling onedimensional access methods to be exploited, has been suggested in the literature but for the most part interest has been confined to the Zorder curve. The possibility of using other curves, such as the Hilbert and Graycode curves, whose characteristics differ from those of the Zorder curve, has also been suggested. In this thesis we design and implement a working le store which is underpinned by the principle of mapping multidimensional data to one of a variety of spacefilling curves and their variants. Data is then indexed using a B+ Tree which remains compact, regardless of the volume and number of dimensions. The implementation has entailed developing
Fast construction of kNearest Neighbor Graphs for Point Clouds
"... Abstract—We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space ..."
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Cited by 10 (1 self)
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Abstract—We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space usage. (3) Better cache efficiency. (4) Ability to handle large data sets. (5) Ease of parallelization and implementation. If the point set has a bounded expansion constant, our algorithm requires one comparison based parallel sort of points according to Morton order plus near linear additional steps to output the knearest neighbor graph. Index Terms—Nearest neighbor searching, point based graphics, knearest neighbor graphics, Morton Ordering, parallel algorithms. 1
Indexing moving objects using shortlived throwaway indexes
 In Proc. SSTD
, 2009
"... Abstract. With the exponential growth of moving objects data to the Gigabyte range, it has become critical to develop effective techniques for indexing, updating, and querying these massive data sets. To meet the high update rate as well as low query response time requirements of moving object appli ..."
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Cited by 7 (1 self)
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Abstract. With the exponential growth of moving objects data to the Gigabyte range, it has become critical to develop effective techniques for indexing, updating, and querying these massive data sets. To meet the high update rate as well as low query response time requirements of moving object applications, this paper takes a novel approach in moving object indexing. In our approach we do not require a sophisticated index structure that needs to be adjusted for each incoming update. Rather we construct conceptually simple shortlived throwaway indexes which we only keep for a very short period of time (subseconds) in main memory. As a consequence, the resulting technique MOVIES supports at the same time high query rates and high update rates and trades this for query result staleness. Moreover, MOVIES is the first main memory method supporting timeparameterized predictive queries. To support this feature we present two algorithms: nonpredictive MOVIES and predictive MOVIES. We obtain the surprising result that a predictive indexing approach — considered stateoftheart in an externalmemory scenario — does not scale well in a main memory environment. In fact our results show that MOVIES outperforms stateoftheart moving object indexes like a mainmemory adapted B xtree by orders of magnitude w.r.t. update rates and query rates. Finally, our experimental evaluation uses a workload unmatched by any previous work. We index the complete road network of Germany consisting of 40,000,000 road segments and 38,000,000 nodes. We scale our workload up to 100,000,000 moving objects, 58,000,000 updates per second and 10,000 queries per second which is unmatched by any previous work. 1
SpatioTemporal aCCESS mETHODS . . .
"... In spatiotemporal applications, moving objects detect their locations via locationaware devices and update their locations continuously to the server. With the ubiquity and massive numbers of moving objects, many spatiotemporal access methods are developed to process user queries efficiently. Spa ..."
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Cited by 7 (0 self)
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In spatiotemporal applications, moving objects detect their locations via locationaware devices and update their locations continuously to the server. With the ubiquity and massive numbers of moving objects, many spatiotemporal access methods are developed to process user queries efficiently. Spatiotemporal access methods are classified into four categories: (1) Indexing the past data, (2) Indexing the current data, (3) Indexing the future data, and (4) Indexing data at all points of time. This short survey IS
The Paradigm of Relational Indexing: A Survey
 In BTW, volume 26 of LNI. GI
, 2003
"... In order to achieve efficient execution plans for queries comprising userdefined data types and predicates, the database system has to be provided with appropriate index structures, query processing methods, and optimization rules. Although available extensible indexing frameworks provide a gatew ..."
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Cited by 4 (1 self)
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In order to achieve efficient execution plans for queries comprising userdefined data types and predicates, the database system has to be provided with appropriate index structures, query processing methods, and optimization rules. Although available extensible indexing frameworks provide a gateway to seamlessly integrate userdefined access methods into the standard process of query optimization and execution, they do not facilitate the actual implementation of the access method itself. An internal enhancement of the database kernel is usually not an option for database developers.